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  4. The distances of two satellites from the surface of the earth are R and 7 R. Their time periods of rotation are in the ratio

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Q. The distances of two satellites from the surface of the earth are $R$ and $7 R$. Their time periods of rotation are in the ratio

Gravitation

Solution:

As $T^{2} \propto r^{3}$,
where $r=$ distance from the centre of the earth.
$\therefore \frac{T_{1}}{T_{2}}=\left(\frac{r_{1}}{r_{2}}\right)^{3 / 2}$
Here, $r_{1}=2 R, r_{2}=8 R$
$\therefore \frac{T_{1}}{T_{2}}=\left(\frac{2 R}{8 R}\right)^{3 / 2}=\frac{1}{4^{3 / 2}}=\frac{1}{8}$